European leaders have a lot to deal with. The financial crisis has prompted several national stimulus packages and a joint effort to keep Greece afloat, while the EU is in danger of being outstripped by other economies that are growing faster, producing more efficiently and at lower costs.

One bright spot is that politicians remain committed to responding to global warming. Unfortunately, their plans do not withstand scrutiny. New research shows that the EU's "20/20/20" policy, which aims to cut greenhouse gas emissions to 20 per cent below 1990 levels by 2020 (and ensure 20 per cent renewable energy), will cost hundreds of billions of euros but yield only tiny benefits. The UK alone will be hit to the tune of an annual 35 billion euros (£28 billion).

As a cost-benefit analysis by the climate-change economist Richard Tol shows, any single regional carbon-reduction scheme will have a very small effect on emissions and temperature rises across the globe. That's not an argument against ever implementing one: but it means that it's crucial that the numbers stack up.

The EU recently stated that it would cost £39 billion a year to meet its emissions target. That figure is implausibly optimistic. Averaging out the best-regarded economic models shows that, even if politicians got their policies exactly right, the cost would come to at least £90 billion a year.

And Europe has not got it exactly right. Instead, it has made things worse, by introducing additional red tape, complication and constraints – in particular, that 20 per cent renewable-energy target. This is expensive because popular "green" energy sources such as wind and solar power cost more than replacing coal with gas. As a result, the real cost of EU policy is likely to be as much as £170 billion.

In his study for the Copenhagen Consensus Centre, Tol assessed the net economic benefits of this policy. Using the conventional estimate that one ton of carbon dioxide is likely to cause about $7 (£4.50) of damage, he found that the total benefit of the EU policy was just £5.7 billion. In other words, every euro spent is likely to generate just three cents' worth of benefits. My research shows that by the end of this century, the EU's approach will reduce temperature rises by approximately 0.05C – almost too small to measure.

The tragedy is that the EU could do much better for the world, and for itself. For far less than £8 billion a year the EU could halve the incidence of malaria, provide micronutrients (particularly vitamin A and zinc) to 80 per cent of the world's undernourished children and prevent a million deaths from TB.

EU leaders should not abandon the fight against climate change. But instead of wasting vast sums on a pointless policy, they should invest in developing green-energy alternatives. The reason it costs so much to reduce carbon emissions is that the green alternatives aren't close to being ready to replace oil and other fossil fuels. Change this, by investing in R& D, and the global impasse over climate change disappears. If we had affordable green-energy sources, everyone – including China and India – would buy them, and long-term emissions would drop significantly.

What Europe must not do is continue to barrel down a path that makes no economic sense. Yet it seems committed to its reckless course. The European Commission wants to toughen the carbon-reduction target to 30 per cent below 1990 levels – which Tol calculates would cost roughly £370 billion a year, twice as much as the existing plans. The effect, over the next 90 years, would be to reduce temperatures by an additional one-hundredth of a degree.

Expensive, poorly conceived carbon-emission plans such as the EU's will cause major economic damage and political strife, while doing little to slow global warming. Europe must change course.